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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 26
ADVANCES IN COMPUTATIONAL MECHANICS Edited by: M. Papadrakakis and B.H.V. Topping
Paper II.1
Computational Structural Stability W.B. Krätzig
Research Centre for Structural Dynamics, Ruhr-University Bochum, Germany , "Computational Structural Stability", in M. Papadrakakis, B.H.V. Topping, (Editors), "Advances in Computational Mechanics", Civil-Comp Press, Edinburgh, UK, pp 21-32, 1994. doi:10.4203/ccp.26.2.1
Abstract
The present paper describes a general structural stability theory
for discretized systems. Instabilities are essential constituents of
nonlinear structural responses, the computational assessment of
which is exclusively based on incremental-iterative (step-wise)
numerical techniques, applied to the tangential equation of motion.
The paper derives this fundamental equation as first variation
of the nonlinear equation of motions in its standard form and
its phase transformation. Further, it transforms the principle of
virtual work for arbitrary nonlinear (Kelvin-Voigt-) continua into
its incremental variant and finally into the consistent tangential
equation of motion. Its application then is demonstrated to classes
of time-independent and time-dependent, unstable structural responses,
all illustrated by several examples.
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